We didn't know it at the time, but in a tiny Edinburgh fringe venue in August 2001, the forthcoming decade was given a sneak preview. The sketch show Rubbernecker featured four little-known talents: Robin Ince, Stephen Merchant, Jimmy Carr and Ricky Gervais – familiar, if at all, from Channel 4's 11 O'Clock Show, which also let Sacha Baron Cohen off his leash. Merchant and Gervais's sitcom The Office had recently screened on BBC2, but it was a sleeper hit and had yet to wake. Carr's smooth ascent to game-show ubiquity had barely begun.

Elsewhere in town, I was reviewing a young double-act called Mitchell and Webb, and – performing in a cellar – a promising character comic, Catherine Tate. The previous year, the Boosh (not yet Mighty) had played the Pleasance; in 2002, Mat (Gavin and Stacey) Horne starred as one half of short-lived twosome Mat and Mackinnon. The decade brought celebrity for all of the above, but withheld it from my own 2001 favourites: art/comedy duo Noble and Silver, comic-theatre maestros Peepolykus, and the performer Alice Lowe, whose work on Garth Marenghi's Netherhead is forever overlooked when people talk about female winners of the Edinburgh comedy award.

That same summer, controversy raged over the Brass Eye paedophile special, Chris Morris's dark masterpiece that talked Nonce Sense about tabloid witch-hunts. With its intelligence, moral disgust, and its scorn of celebrity, Brass Eye now seems like the relic of a bygone era: in the years since, British comics (with a few exceptions) have seemed terrified of politics. It was left to Americans Michael Moore (at the Roundhouse in London in 2002) and Doug Stanhope to remind us that speaking truth to power can equal electrifying standup.

Still, the Brass Eye hoo-ha set the tone for a decade in which comedy became the nation's moral barometer – even if the "offensive" acts to come weren't always as defensible as Morris. Gervais was a key player. The Office rejuvenated the sitcom, combining Spinal Tap's documentary form with the foot-in-mouth, near-the-knuckle content of Larry David's Curb Your Enthusiasm. Like its successor, Extras, it made hay with liberal anxieties surrounding political correctness. Jimmy Carr, Little Britain and in the US, the skilful Sarah Silverman, followed suit.

Increasingly, the battle lines were drawn between good (legitimate, questioning) offence and bad (boorish) offence. But few agreed which jokes belonged on which side. Billy Connolly wisecracking about Iraq hostage Ken Bigley? Stewart Lee directing the Christian-baiting musical Jerry Springer the Opera? At least these were debates worth having, which demonstrated the vitality of comedy. The same can't be said of our squabbles at the decade's end. Whoever you blame – tabloids, overcautious broadcasters, thuggish comics – the fact that comedy's cause celebres are now routines about Rebecca Adlington's looks and Russell Brand's prank phone-calls suggest the nadir has been reached.

Hence the counter-reaction – which is where Robin Ince comes back in. Ince is nerd-in-chief of another strand in noughties comedy: the rise of bookish, lo-fi whimsy. The younger generation of comics – who include 2002 Perrier award winner Daniel Kitson, Josie Long and recent Edinburgh comedy award winner Tim Key – are pioneering a brand of standup that wishes no offence to anyone. Soulfulness, curiosity and invention are key; jokes sometimes less so. Of the movement's standard bearers, only the terrific New Zealand musical act Flight of the Conchords and boffin New Yorker Demetri Martin have yet made the leap into mainstream success. More will follow.

For most of the decade, an online comedy revolution has been just around the corner. So far, that's where it stays. Yes, YouTube and MySpace has helped younger comics sell themselves, and the odd bedroom-based career has been launched. But instant online ubiquity is a curse as well as a blessing: witness recent anxieties about plagiarism, bootlegs and the drastically reduced shelflife of new jokes.

Finally, the story of comedy hasn't been digital, it's been live. As Peter Kay's record-breaking ticket sales proved last month, standup is booming. If early 90s comedy was the new rock'n'roll, today it's the new football. We follow it en masse (live and on TV); we've all got our favourites and our hate-figures; we are forever frustrated by the frequent scandals that give the game a bad name. At least there's no need to bid for the World Cup: when it comes to comedy, Britain is the permanent international host. At the end of the decade, it's increasingly large audiences who are doing the rubbernecking.